There is a certain bookshelf speaker sys that some are recomending upgrading the tweeter to a particular high quality one and adding a 12uf cap to it.
My dumb question is, how would the cap be wired to the tweeter?

First be very skeptical.
12uf @ 8Ω = 1650Hz = Blown up tweeter.
12uf @ 4Ω = 3300Hz = Blown up tweeter if the power is too high.
Most tweeters don't like getting pushed lower than 2000Hz @ 6db/octave slope (which is what you have with just a capacitor in series to the positive pole of the tweeter).
If the speaker has a second order crossover (Series Cap w/ Parallel Inductor to the tweeter) I would ONLY recommend a 4Ω tweeter.
The crossover point would be around 1700Hz.
There are many high quality 4Ω tweeters that will behave properly @ 1700Hz.
The second order crossover attenuates at 12db/octave.
This combined with most large dome tweeters' natural roll off can sometimes equal a third order (18db/octave) acoustic roll off.

Please get more information and pay very close attention to tweeter specifications before driving the speaker.

You would connect the capacitor between the amp and one terminal of the tweeter. The other terminal of the tweeter would go straight to the amp. The cap would typically go to the positive terminal of the amp, but the polarity of the tweeter depends on what goes best (sounds best) and won't cause any damage if you get it wrong.

If others have said it sounds good then perhaps it does. You won't be able to get too loud with it but if you're unsatisfied you can always change things around.

This is a tweeter that you will crossover at 12db/octave and pray.
This tweeter has a 1350hz resonant frequency.
A safe rule of thumb is to double the resonant for 12db/octave and at least triple for 6db/octave.
With the crossover point at 2nd order Lw/Ri 1700Hz you might obtain close to a 18db/octave acoustic roll off and the tweeter may be OK.
But remember, a driver moves, woofers just move more.
When a driver reaches its resonant frequency it will move a much longer distance to recreate the same amount of sound.
When tweeters move too much they blow up.
If you want to try this just start with your amp at minimum volume and SLOWLY turn up the volume with your ear to the tweeter.
If you start to hear the slightest crackling STOP, driving a tweeter beyond this point may destroy it.
I personally have looked at this tweeter for two projects but neither crossed the tweeter below 3500Hz 2nd order Lw/Ri.

I once used tweeters this way (single capacitor within 3 octaves of fs). I wouldn't do it this way any more but it did hold a certain charm for me at the time. Tweeters need to be at the right level and using a resistor for this purpose is neither here nor there with regards to how it works... if you need it then you need it, and if you do then the capacitor may need to be adjusted to suit.

One thing I'd do if I were going this way again is to implement a resonance peak filter so that the impedance doesn't overwhelm the capacitor giving you a peak near resonance.

It is a 4 ohm unit which broadly suggests any capacitor will be twice as large as an equivalent 8 ohm compatible capacitor.

If you like the sound of the woofer enough to work on this unit, you might check the damping inside the box, choose a crossover point and roll the woofer off a little. These issues and others are probably more of a concern than any worries about going second order with the tweeter.